NORMAL PROCESSES OF ENERGY METABOLISM 599 



sible for the first demonstrations of the applicability of the law. Rubner 

 worked with dogs of adult stature but widely different size, estimating their 

 metabolism by the indirect method. Richet worked first with rabbits 

 langing from 2000 to 3500 grams in weight but he determined only the 

 heat of radiation and conduction, neglecting, as nearly all subsequent 

 French observers have done, the heat given off by evaporation. Naturally 

 his quantities would be more nearly proportional to surface than the total. 

 However, in the estimation of surfaces he says, "If one supposes that 

 animals of different size are like spheres of different volumes, then the 

 respective volumes are related among themselves as the cubes of their 

 radii; while the respective surfaces are related among themselves as the 

 squares of their radii. These considerations apply to living animals, and, 

 since their form is so irregular compared with that of a perfect sphere, 

 one can only apply the geometrical facts to them approximately." Fur- 

 ther in summing up the factors which determine heat production Richet 

 notes that one of these is "the nature of the integument." In two im- 

 portant respects, therefore, Richet made saving clauses regarding the 

 application of the law of surface, one concerning the measurement of 

 surface and the other concerning the nature of the skin, meaning, of 

 course, its conducting properties. Rubner in the beginning considered 

 that he had demonstrated the law only for adult animals and later in 

 applying it to children made this very emphatic reservation : "The law 

 of surface area holds under all physiological conditions of life, but for its 

 proof it is a reasonable presumption that only organisms of similar 

 physiological capacities,- as regards nutrition, climatic influences, tem- 

 perament, and functional power, should be compared." Other students of 

 metabolism have made similar reservations. Thus Schlossmann says, "The 

 presumption is on the one hand that the environment is relatively normal, 

 on the other that the child has a relatively normal surface, that is, a 

 functioning and good conducting skin with the normal amount of sub- 

 cutaneous fat." Otherwise, he thinks, the law could not be expected 

 to apply. 



The arguments against the law, so far as they rest upon facts, seem, 

 as we have just seen, to have been misconceived. It never was supposed 

 by its chief proponents that the law would apply to all physiological and 

 pathological conditions but only to similar physiological (normal) condi- 

 tions. Also, a very superficial understanding of the necessary mathematical 

 relations shows that the law has natural limitations which must be recog- 

 nized if one is to avoid compromising it with impossible conditions. 



There is no doubt that Rubner, following Bergmann, has conceived 

 of the law as causally related to Newton's law of cooling. This dependence 

 as commonly accepted may be phrased in this way. Solid bodies when 

 warmed lose heat in proportion to the difference between the temperature 

 of the body and the temperature of the surrounding medium. Since this 



